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Get the taxonomy value in the post loop inside the archive page

sorry for my noob code but it feels close to what I am trying to achieve. I need help on displaying the taxonomy values inside the archive post loop. I have a custom post type called "plays" and there are custom taxonomies tied to it called "leagues" and "systems". There are multiple kinds of ‘leagues’ and ‘systems’ but I need to show only the ones that are in each post. Here is the code:

<?php if( have_posts() ): while( have_posts() ): the_post();?>
                            <div class="row pick-row">
                                <div class="col-md-4 valign">
                                    <div class="row">
                                        <div class="col-md-6 col-6 pb-4">
                                            <p class="pick-date"><b><?php the_field('date');?></b></p>
                                            <h2>
                                                <?php the_title();?>
                                            </h2>
                                        </div>
                                        <div class="col-md-6 col-6 pb-4">
                                            <div class="model-league">
                                                <p>
                                                    <b>Model</b>
                                                </p>
                                                <?php
                                                     
                                                    // Get the taxonomy's terms
                                                    $terms = get_terms(
                                                        array(
                                                            'taxonomy'   => 'system',
                                                            'hide_empty' => true,
                                                        )
                                                    );

                                                    // Check if any term exists
                                                    if ( ! empty( $terms ) && is_array( $terms ) ) {
                                                        // Run a loop and print them all
                                                        foreach ( $terms as $term ) { ?>
                                                            <a href="<?php echo esc_url( get_term_link( $term ) ) ?>">
                                                                <?php echo $term->name; ?>
                                                            </a><?php
                                                        }
                                                    } 
                                                     
                                                 ?>
                                                
                                                
                                                <p>
                                                    <b>League</b>
                                                </p>
                                                
                                                <?php
                                                     
                                                    // Get the taxonomy's terms
                                                    $terms = get_terms(
                                                        array(
                                                            'taxonomy'   => 'leagues',
                                                            'hide_empty' => true,
                                                        )
                                                    );

                                                    // Check if any term exists
                                                    if ( ! empty( $terms ) && is_array( $terms ) ) {
                                                        // Run a loop and print them all
                                                        foreach ( $terms as $term ) { ?>
                                                            <a href="<?php echo esc_url( get_term_link( $term ) ) ?>">
                                                                <?php echo $term->name; ?>
                                                            </a><?php
                                                        }
                                                    } 
                                                     
                                                 ?>
                                                
                                            </div>
                                        </div>
                                    </div>
                                    
                                </div>
                                <div class="col-md-6">
                                    <div class="row picks-details">
                                        <div class="col-md-3 col-6 pb-4">
                                            <h2>
                                                Selection
                                            </h2>
                                            <span>
                                                <?php the_field('selection');?> 
                                            </span>
                                        </div>
                                        <div class="col-md-3 col-6 pb-4">
                                            <h2>
                                                Odds
                                            </h2>
                                            <span>
                                                <?php the_field('odds');?> 
                                            </span>
                                        </div>
                                        <div class="col-md-3 col-6 pb-4">
                                            <h2>
                                                Stake
                                            </h2>
                                            <span>
                                                <?php the_field('stake');?> 
                                            </span>
                                        </div>
                                        <div class="col-md-3 col-6 pb-4">
                                            <h2>
                                                Units
                                            </h2>
                                            <span>
                                                <?php the_field('units');?> 
                                            </span>
                                        </div>
                                    </div>

                                </div>
                                <div class="col-md-2 pb-4 valign text-center text-md-right">
                                    <a class="btn btn-main" href="<?php the_permalink();?>"">
                                        Details
                                    </a>
                                </div>
                                <div class="col-md-12">
                                    <hr>
                                </div>
                            </div>
                        <?php endwhile; else: endif;?>